Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-6y &= -1 \\ 3x+6y &= -6\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = -6y-6$ Divide both sides by $3$ to isolate $x$ $x = {-2y - 2}$ Substitute this expression for $x$ in the first equation. $2({-2y - 2}) - 6y = -1$ $-4y - 4 - 6y = -1$ Simplify by combining terms, then solve for $y$ $-10y - 4 = -1$ $-10y = 3$ $y = -\dfrac{3}{10}$ Substitute $-\dfrac{3}{10}$ for $y$ in the top equation. $2x-6( -\dfrac{3}{10}) = -1$ $2x+\dfrac{9}{5} = -1$ $2x = -\dfrac{14}{5}$ $x = -\dfrac{7}{5}$ The solution is $\enspace x = -\dfrac{7}{5}, \enspace y = -\dfrac{3}{10}$.